一种方向优化最小均方算法

最小均方(Least Mean Square, LMS)算法的更新方向是对最速下降方向的估计，其收敛速度也受到最速下降法的约束。为了摆脱该约束，该文在对LMS算法分析的基础上，提出一种针对LMS算法的分块方向优化方法。该方法通过分析误差信号来选择更新向量，使得算法的更新方向尽可能接近Newton方向。基于此方法，给出一种方向优化LMS(Direction Optimization LMS, DOLMS)算法，并推广到变步长DOLMS算法。理论分析与仿真结果表明，该方法与传统分块LMS算法相比，有更快的收敛速度和更小的计算复杂度。

A Direction Optimization Least Mean Square Algorithm

The update vector of Least Mean Square (LMS) algorithm is an estimation of the gradient vector, thus its convergence rate is limited by the method of steepest descent. Based on the discussion of basic LMS, a direction optimization method of LMS algorithm is proposed in order to get rid of this speed constraint. In the proposed method, the closest update vector to the Newton direction is chosen based on the analysis of the error signal. Based on the method, a Direction Optimization LMS (DOLMS) algorithm is proposed, and it is extended to the variable step-size DOLMS algorithm. The theoretical analysis and the simulation results show that the proposed method has higher speed of convergence and less computational complexity than traditional block LMS algorithm.